Question

Given vectors u = ⟨–5, 1⟩ and v = ⟨8, 6⟩, which statement is true for u and v?

The vectors point in the same direction.
The vectors form an acute angle.
The vectors form an obtuse angle.
The vectors point in opposite directions.

Answer 1

Answer:

The vectors form an obtuse angle.

Step-by-step explanation:

On a graph, -5, 1 is in the second quadrant and 8, 6 is in the first. The angle about the orgin is obtuse.

Finding the dot product between them results in a negative, which also means the angle is obtuse.

Answer 2

The two vectors mentioned here: u = ⟨–5, 1⟩ and v = ⟨8, 6⟩ form an obtuse angle.

What is an obtuse angle?

When the value of an angle is greater than 90 degrees and less than 180 degrees, than that angle is called an obtuse angle.

Given,

u = (-5i + j)

v = (8 + 6j)

Let, the angle between these two vectors = Ф

Therefore, cos Ф = (u.v)/(|u| |v|)

⇒ cos Ф = [(-5i + j).(8i + 6j)]/[|(-5i + j)| |(8 + 6j)|]

⇒ cos Ф = [-40+6]/[√26 √100]

⇒ cos Ф = [-34]/10√26

⇒ cos Ф = -0.67

⇒ Ф = cos⁻¹(0.67.) = 132°

Therefore, the two vectors form an obtuse angle.

Hence, Option(C) is the correct answer.

Learn more about an obtuse angle here: https://brainly.com/question/17755276

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